Kodaira's table of singular fibers has a singular fiber for each of $\tilde{A}_n$, $\tilde{D}_n$, $\tilde{E}_6$, $\tilde{E}_7$, and $\tilde{E}_8$; these are chains or cycles of (-2)-curves connected to each other based on the aforementioned Dynkin diagram.

On the other hand $A_n$, $D_n$, $E_6$, $E_7$, and $E_8$ Dynkin diagrams, by McKay correspondence, describe the exceptional curves of quotient singularities; i.e. if $G$ is a finite group corresponding to one of these Dynkin diagrams, $\mathbb{C}^2/G$ has a resolution whose exceptional curve is equal to that Dynkin diagram.

Question: Is there a similar construction of Kodaira's singular fibers? i.e. can we obtain them as a resolution of some quotient prescribed by one of $\tilde{A}_n$, $\tilde{D}_n$, $\tilde{E}_6$, $\tilde{E}_7$, and $\tilde{E}_8$.